The present invention relates to attitude control for geosynchronous satellites and, more particularly, to attitude control systems and methods for compensating roll and yaw pointing errors that occur as a consequence of orbit deviation from the nominal equatorial orbit plane.
Communications and navigation satellites are typically placed in a circular orbit, known as a geosynchronous or geostationary orbit, having a period of revolution equal to that of the earth to provide synchronized rotational velocities. Ideally, the satellite is placed in an orbit plane coincident with the equatorial plane of the earth so that the antenna or antennas of the satellite can be pointed to desired terrestrial locations. In general, geosynchronous satellites are momentum stabilized, either by spinning the satellite itself or providing a momentum wheel, with the spin axis maintained normal the desired equatorial orbit plane and the global beam boresight aligned normal to the spin axis. In this ideal situation, the global beam boresight points to a subsatellite area that remains fixed as the satellite and earth rotate in synchronism.
Several factors induce orbital drift by which the satellite orbit tilts relative to the nominal equatorial orbit plane. This orbit tilt, which accumulates with time, creates roll and yaw pointing errors. More specifically, the gravitational effect of the sun and the moon on the satellite and the variations in the earth's gravitational field caused by the non-spherical shape of the earth introduce orbit perturbing effects which cause the plane of the satellite's orbit to tilt with respect the desired equatorial plane. The net effect of these orbit-disturbing influences is to cause the inclination of the satellite orbit to drift slowly at a rate of between 0.75.degree. and 0.95.degree. per year.
As the orbit inclination increases, the terrestrial illumination pattern of the satellite's antenna or antennas drifts from the desired aiming area as a consequence of the roll and yaw pointing errors. For example and as shown in FIGS. 1 and 2, a satellite `S` moving in an earth orbit in the direction indicated at an angle i to the equatorial orbit plane will intersect the equatorial plane at an ascending node N.sub.a where the satellite passes from the southern hemisphere to the northern hemisphere and again intersect the equatorial orbit plane at the descending node N.sub.d when moving from the northern hemisphere to the southern hemisphere. As the satellite progresses from its ascending node N.sub.a to its maximum northern latitude, it passes through its north anti-node N.sub.n, and, conversely, as the satellite progresses from its descending node N.sub.d to its maximum southern latitude, it passes through its south anti-node N.sub.s.
As a consequence of the inclination angle i between the actual satellite orbit and the nominal equatorial plane, the antenna illumination pattern that the satellite projects onto the surface of the earth will suffer from the adverse effects of sinusoidal variations of the north-south and rotational motions, corresponding to the spacecraft roll error and yaw errors, respectively. For example, in the case where the satellite spin axis is normal to the inclined orbit plane, as shown in FIG. 2, as the satellite progresses through its ascending node N.sub.a, the roll error (FIG. 3A) of the terrestrial illumination pattern is zero while the yaw error (FIG. 3)) is at a maxima. As the satellite progresses towards its north anti-node N.sub.n, the roll error increases until attaining a maxima at the north anti-node N.sub.n while the yaw error reduces to zero. As shown in FIG. 2, when the satellite is at its north anti-node N.sub.n, the global beam boresight will be directed to point S.sub.1 on the earth's surface. Conversely, as the satellite progresses from the north anti-node N.sub.n, the roll error diminishes to zero and the yaw error once again increase to a maxima at the descending node N.sub.d. When the satellite attains its south anti-node N.sub.s, as shown in FIG. 2, the global beam boresight will be directed to point S.sub.2 on the earth's surface.
The roll and yaw errors introduced by orbit inclination depend on the orientation of the spacecraft spin axis. In the general case where the spin axis is tilted by an angle .alpha. from the axis normal to the equatorial plan, the roll error will be (1.178i-.alpha.) SIN nt and the yaw error will by -.alpha. COS nt, where i is the orbit inclination, n is the orbit angular rate, and t=time with t=0 at the ascending node. As can be appreciated roll and yaw error are functionally related and one can be determined as a function of the other.
One technique proposed for the reduction of the roll pointing error is to intentionally tilt the vehicle spin axis relative to the equatorial orbit normal. As shown in FIG. 2, the satellite spin axis (dotted line illustration) is tilted at an angle .theta. to effectively reposition the global beam boresight of the satellite to the area S.sub.o obtained with the satellite in the equatorial orbit. While the roll error will be effectively zero, the yaw error will be increased by the contribution of the spin axis tilt angle .theta. and is represented by -(i+.theta.) COS nt. Where circularly polarized communications or narrow spot beams are utilized, tee increased yaw error is unacceptable.
In conventional satellite systems, thrusters are used to periodically correct the inclination of the orbit by expending fuel, this use being termed north-south station-keeping. In particular and for a ten-year mission, this station-keeping function can require as much as 20% of the total initial mass of the satellite with a substantial fraction of the propellant, approximately 90%, used for orbit inclination correction and the remainder used for other in-orbit maneuvers including attitude error correction (FIG. 3C). In general, the operating life of a geosynchronous satellite is limited by the station-keeping fuel requirements and operating life can be extended by terminating north-south station-keeping. However, cessation of north-south station-keeping introduces attitude errors which must be corrected.
In recognition of the substantial on-board fuel requirements for inclination correction maneuvers, various attitude control systems have been proposed to correct attitude errors introduced by orbit inclination. For example, U.S. Pat. No. 4,084,772 to Muhlfelder presents a system for roll/yaw vehicle steering in which the vehicle is stabilized by a momentum wheel in which angular velocity of the wheel is varied in a sinusoidal manner during the course of the orbit revolution to vary the associated vehicle momentum and effect a sinusoidal variation in the roll attitude of the vehicle with each orbit revolution. In U.S. Pat. No. 4,062,509 to Muhlfelder et al., a magnetic torquing system is provided by which a vehicle magnetic field is established to interact with the earth's magnetic field to provide a measure of roll and yaw attitude control.